Diffusing-wave spectroscopy: Difference between revisions

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Revision as of 20:23, 10 August 2010

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'''Diffusing-wave spectroscopy''' (DWS) is an optical technique derived from [[dynamic light scattering]] (DLS) that studies the dynamics of scattered light in the limit of strong multiple scattering.<ref>

{{cite journal

<ref>G. Maret and P. E. Wolf, Z. Phys. B: Condens. Matter 65, 409 1987</ref>

|author=G. Maret, P. E. Wolf

<ref>D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 1988</ref>

|year=1987

It has been widely used in the past to study colloidal [[suspension]]s, [[emulsions]], [[foams]], gels, biological media and other forms of [[soft matter]]. If carefully calibrated, DWS allows the quantitative measurement of microscopic motion in a soft material, from which the [[rheological]] properties of the complex medium can be extracted ''via'' the so-called [[microrheology]] approach.

|title=

|journal=[[Zeitschrift für Physik B: Condensed Matter]]

|volume=65 |pages=409

}}</ref><ref>

{{cite journal

<ref> |author=D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 1988</ref>

|year=1988

|title=

|journal=[[Physical Review Letters]]

|volume=60 |pages=1134

|doi=

}}</ref> It has been widely used in the past to study colloidal [[suspension]]s, [[emulsions]], [[foams]], gels, biological media and other forms of [[soft matter]]. If carefully calibrated, DWS allows the quantitative measurement of microscopic motion in a soft material, from which the [[rheological]] properties of the complex medium can be extracted ''via'' the so-called [[microrheology]] approach.

==One-speckle diffusing-wave spectroscopy==

Line 14 ⟶ 26:

<math>g_2(\tau)=\frac{<I(t)I(t+\tau)>_t}{<I(t)>_t^2}</math>

For the case of non-interacting particles suspended in a (complex) fluid a direct relation between g₂-1 and the mean square displacement of the particles <Δr²> can be established. Let's note P(s) the probability density function (PDF) of the photon path length s. The relation can be written as follows:<ref>
{{cite journal
|author=F. Scheffold, S.''et Romer, Fal. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa1, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti and P. Schurtenberger, ''
|year=2004
|title=New trends in optical microrheology of complex fluids and gels,
|journal=[[Progress in Colloid and Polymer Science, vol ]]
|volume=123/2004, pp |pages=141-146</ref> <br />

|doi=

<math>g_2(\tau)-1=[\int {ds P(s) exp(-(s/l*)k_0^2 <\Delta r^2(\tau)>) }]^2</math><br />

}}</ref>

<math>g_2(\tau)-1=[\int {ds P(s) exp(-(s/l*)k_0^2 <\Delta r^2(\tau)>) }]^2</math><br />

with <math>k_0=\frac{2\pi n}{\lambda}</math> and <math>l*</math> is the transport mean free path of scattered light.

For simple cell geometries, it is thus possible to calculate the mean square displacement of the particles <Δr²> from the measured g₂-1 values analytically. For example, for the backscattering geometry, an infinitely thick cell, large laser spot illumination and detection of photons coming from the center of the spot, the relation ship between g₂-1 and <Δr² is :<br />

<math>g_2(\tau)-1=exp[-2 \gamma \sqrt{<\Delta r^2(\tau)>k_0^2}]</math>, γ value is around 2.

For less thick cells and in transmission, the relationship depends also on l* (the transport length)<ref>D. A. Weitz and D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light scattering, W. Brown, ed., Clarendon Press, Oxford (1993) 652–720</ref>.

{{cite book

|author=D. A. Weitz, D. J. Pine

|year=1993

|chapter=Diffusing-wave spectroscopy

|editor=W. Brown

|title=Dynamic Light scattering

|pages=652–720

|publisher=[[Clarendon Press]]

|isbn=9780198539421

}}</ref>

==Multispeckle Diffusing-Wave Spectroscopy (MSDWS)==

Line 32 ⟶ 65:

<math>g_2(\tau)=\frac{<I(t)I(t+\tau)>_p}{<I(t)>_p^2}</math>

MSDWS is particularly adapted for the study of slow dynamics and non ergodic media. Echo-DWS allows seamless integration of MSDWS in a traditional DWS-scheme with superior temporal resolution down to 12ns <ref>Multispeckle diffusing-wave spectroscopy with a single-mode detection scheme, P12&nbsp;ns. Zakharov, F. Cardinaux, and F. Scheffold, Phys. Rev. E 73, 011413 (2006) http://link.aps.org/doi/10.1103/PhysRevE.73.011413]</ref>. Camera based adaptive image processing

{{cite journal

<ref>L. Brunel, A. Brun, P. Snabre, and L. Cipelletti, Optics Express, Vol. 15, Issue 23, pp. 15250-15259 [http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-23-15250]</ref> [http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-23-15250]

|author=P. Zakharov, F. Cardinaux, and F. Scheffold

allows online measurement of particle dynamics for example during drying.

|year=2006

|title=Multispeckle diffusing-wave spectroscopy with a single-mode detection scheme

|journal=[[Physical Review E]]

|volume=73 |pages=011413

|doi=10.1103/PhysRevE.73.011413

}}</ref> Camera based adaptive image processing allows online measurement of particle dynamics for example during drying.<ref>

{{cite journal

|author=L. Brunel, A. Brun, P. Snabre, and L. Cipelletti

|title=

|url=http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-23-15250

|journal=[[Optics Express]]

|volume=15 |issue=23 |pages=15250-15259

|doi=

}}</ref>

==References==

{{reflist}}

<references/>

==External links==

* Formulation SA, France [http://www.formulaction.com/]

*LSInstruments GmbH, Switzerland [http://www.lsinstruments.ch/]

[[Category:Physics]]

[[Category:Optics]]